Nanopore gates via reversible crosslinking of polymer brushes: a theoretical study.

Polymer-brush-modified nanopores are synthetic structures inspired by the gated transport exhibited by their biological counterparts. This work theoretically analyzes how the reversible crosslinking of a polymer network by soluble species can be used to control transport through nanochannels and pores. The study was performed with a molecular theory that allows inhomogeneities in the three spatial dimensions and explicitly takes into account the size, shape and conformations of all molecular species, considers the intermolecular interactions between the polymers and the soluble crosslinkers and includes the presence of a translocating particle inside the pore. It is shown than increasing the concentration of the soluble crosslinkers in bulk solution leads to a gradual increase of its number within the pore until a critical bulk concentration is reached. At the critical concentration, the number of crosslinkers inside the pore increases abruptly. For long chains, this sudden transition triggers the collapse of the polymer brush to the center of the nanopore. The resulting structure increases the free-energy barrier that a translocating particle has to surmount to go across the pore and modifies the route of translocation from the axis of the pore to its walls. On the other hand, for short polymer chains the crosslinkers trigger the collapse of the brush to the pore walls, which reduces the translocation barrier.

Structure and dynamics of nanoconfined water and aqueous solutions.

This review is devoted to discussing recent progress on the structure, thermodynamic, reactivity, and dynamics of water and aqueous systems confined within different types of nanopores, synthetic and biological. Currently, this is a branch of water science that has attracted enormous attention of researchers from different fields interested to extend the understanding of the anomalous properties of bulk water to the nanoscopic domain. From a fundamental perspective, the interactions of water and solutes with a confining surface dramatically modify the liquid's structure and, consequently, both its thermodynamical and dynamical behaviors, breaking the validity of the classical thermodynamic and phenomenological description of the transport properties of aqueous systems. Additionally, man-made nanopores and porous materials have emerged as promising solutions to challenging problems such as water purification, biosensing, nanofluidic logic and gating, and energy storage and conversion, while aquaporin, ion channels, and nuclear pore complex nanopores regulate many biological functions such as the conduction of water, the generation of action potentials, and the storage of genetic material. In this work, the more recent experimental and molecular simulations advances in this exciting and rapidly evolving field will be reported and critically discussed.

Nanocompartmentalization of the Nuclear Pore Lumen.

The nuclear pore complex (NPC) employs the intrinsically disordered regions (IDRs) from a family of phenylalanine-glycine-rich nucleoporins (FG-Nups) to control nucleocytoplasmic transport. It has been a long-standing mystery how the IDR-mediated mass exchange can be rapid yet selective. Here, we use a computational microscope to show that nanocompartmentalization of IDR subdomains leads to a remarkably elaborate gating structure as programmed by the amino acid sequences. In particular, we reveal a heterogeneous permeability barrier that combines an inner ring barrier with two vestibular condensates. Throughout the NPC, we find a polarized electrostatic potential and a diffuse thermoreversible FG network featuring mosaic FG territories with low FG-FG pairing fraction. Our theoretical anatomy of the central transporter sheds light into the sequence-structure-function relationship of the FG-Nups and provides a picture of nucleocytoplasmic mass exchange that allows a reconciliation of transport efficiency and specificity.

Dynamic Crowding Regulates Transcription.

The nuclear environment is highly crowded by biological macromolecules, including chromatin and mobile proteins, which alter the kinetics and efficiency of transcriptional machinery. These alterations have been described, both theoretically and experimentally, for steady-state crowding densities; however, temporal changes in crowding density ("dynamic crowding") have yet to be integrated with gene expression. Dynamic crowding is pertinent to nuclear biology because processes such as chromatin translocation and protein diffusion lend to highly mobile biological crowders. Therefore, to capture such dynamic crowding and investigate its influence on transcription, we employ a three-pronged, systems-molecular approach. A system of chemical reactions represents the transcription pathway, the rates of which are determined by molecular-scale simulations; Brownian dynamics and Monte Carlo simulations quantify protein diffusion and DNA-protein binding affinity, dependent on macromolecular density. Altogether, this approach shows that transcription depends critically on dynamic crowding as the gene expression resultant from dynamic crowding can be profoundly different than that of steady-state crowding. In fact, expression levels can display both amplification and suppression and are notably different for genes or gene populations with different chemical and structural properties. These properties can be exploited to impose circadian expression, which is asymmetric and varies in strength, or to explain expression in cells under biomechanical stress. Therefore, this work demonstrates that dynamic crowding nontrivially alters transcription kinetics and presents dynamic crowding within the bulk nuclear nanoenvironment as a novel regulatory framework for gene expression.

Modeling the nucleoporins that form the hairy pores.

Sitting on the nuclear envelope, nuclear pore complexes (NPCs) control the molecular transport between the nucleus and the cytoplasm. Without definite open or close states, the NPC uses a family of intrinsically disordered nucleoporins called FG-Nups to construct a selective permeability barrier whose functional structure is unclear. Experimental advances have offered high-resolution molecular knowledge of the NPC scaffold and docking of the unfolded FG-Nups, however, the 'hairy' barrier structure still appears as blurred lobes even under the state-of-the-art microscopy. Without accurate experimental visualization, the molecular mechanism for the NPC-mediated transport remains a matter of debate. Modeling provides an alternative way to resolve this long-standing mystery. Here, we briefly review different methods employed in modeling the FG-Nups, arranging from all-atom molecular dynamics to mean-field theories. We discuss the advantage and limit of each modeling technique, and summarize the theoretical insights that, despite certain controversy, deepened our understanding of the hairy pore.

Effect of Polymer Surface Modification of Superparamagnetic Iron Oxide Nanoparticle Dispersions in High Salinity Environments.

Superparamagnetic nanoparticles (SPIONs) can be used as nuclear magnetic resonance (NMR) signal enhancement agents for petroleum exploration. This enhancement effect is uniform if SPIONs are monodisperse in size and in composition; yet it is challenging to synthesize monodisperse particles that do not aggregate in high salinity petroleum brine. Here, we report a method to synthesize individual SPIONs coated with tunable surface coating densities of poly(2-acrylamido-2-methyl-1-propanesulfonic acid (pAMPS) with a catechol end-group (pAMPS*). To establish parameters under which pAMPS*-coated SPIONS do not aggregate, we compared computational predictions with experimental results for variations in pAMPS* chain length and surface coverage. Using this combined theoretical and experimental approach, we show that singly dispersed SPIONs remained stabilized in petroleum brine for up to 75 h with high surface density pAMPS*.

Label-free imaging of the native, living cellular nanoarchitecture using partial-wave spectroscopic microscopy.

The organization of chromatin is a regulator of molecular processes including transcription, replication, and DNA repair. The structures within chromatin that regulate these processes span from the nucleosomal (10-nm) to the chromosomal (>200-nm) levels, with little known about the dynamics of chromatin structure between these scales due to a lack of quantitative imaging technique in live cells. Previous work using partial-wave spectroscopic (PWS) microscopy, a quantitative imaging technique with sensitivity to macromolecular organization between 20 and 200 nm, has shown that transformation of chromatin at these length scales is a fundamental event during carcinogenesis. As the dynamics of chromatin likely play a critical regulatory role in cellular function, it is critical to develop live-cell imaging techniques that can probe the real-time temporal behavior of the chromatin nanoarchitecture. Therefore, we developed a live-cell PWS technique that allows high-throughput, label-free study of the causal relationship between nanoscale organization and molecular function in real time. In this work, we use live-cell PWS to study the change in chromatin structure due to DNA damage and expand on the link between metabolic function and the structure of higher-order chromatin. In particular, we studied the temporal changes to chromatin during UV light exposure, show that live-cell DNA-binding dyes induce damage to chromatin within seconds, and demonstrate a direct link between higher-order chromatin structure and mitochondrial membrane potential. Because biological function is tightly paired with structure, live-cell PWS is a powerful tool to study the nanoscale structure-function relationship in live cells.

Insights into the Role of Counterions on Polyelectrolyte-Modified Nanopore Accessibility.

Nanopores play a decisive role in different technologies from oil production, separation, and sensing to drug delivery or catalysis and energy conversion. In recent years, abilities to functionalize nanopores have advanced significantly. Thereby, nanopores functionalized with polyelectrolytes or responsive polymers show fascinating transport properties, such as gated or gradually controlled ionic permselectivity. Nonetheless, understanding the influence of external parameters such as ion type or concentration on nanopore performance, and thus on the mentioned applications, remains a challenge but is crucial for applications. In this work, the effect of different counterions on the wetting and ionic transport in poly(2-(methacryloyloxy)ethyltrimethylammonium chloride)-functionalized silica mesopores (pore diameter <10 nm) was experimentally and theoretically investigated. Static contact angles covered a range from 45 to almost 90° by exclusively changing the counterion. Ionic pore accessibility was also strongly dependent on the counterion present and was found to gradually change from accessible pores up to complete, pH-independent ion exclusion. On the basis of molecular theory calculations, these experimental observations were rationalized on the basis of ion binding between the [2-(methacryloyloxy)ethyl]trimethylammonium chloride monomers and the counterions. In addition, the theoretical framework provided a nanoscopic view into the molecular organization inside the pores, showing a strong dependence of ion concentration and ion distribution profiles along the pore radius in dependence of the present ions. The obtained insights on the role of counterion type and ion binding in nanopores are expected to have direct impact on the above-mentioned applications.

Competitive calcium ion binding to end-tethered weak polyelectrolytes.

We have developed a molecular model to describe the structural changes and potential collapse of weak polyelectrolyte layers end-tethered to planar surfaces and spherical nanoparticles as a function of pH and divalent ion concentration. In particular, we describe the structural changes of polymer-coated nanoparticles end-tethered to copolymers of poly(acrylic acid) (pAA) and poly arcrylamido-2-methylpropane sulfonate (pAMPS) in the presence of Ca2+ ions. We find that end-grafted poly(acrylic acid) layers will collapse in aqueous solutions containing sufficient amounts of Ca2+ ions, while polymers and copolymers with sufficient AMPS monomers will not collapse. The collapse of end-tethered pAA is due to the formation of calcium bridges between two acrylic acid monomers and one calcium ion. On the other hand pAMPS layers do not collapse due to the lack of calcium bridges. The collapse of pAA layers is strongly dependent on the pH as well as divalent and monovalent salt concentrations of the environment. The collapse is also strongly influenced by the curvature of the tethering surface.

The effects of chemical fixation on the cellular nanostructure.

Chemical fixation is nearly indispensable in the biological sciences, especially in circumstances where cryo-fixation is not applicable. While universally employed for the preservation of cell organization, chemical fixatives often introduce artifacts that can confound identification of true structures. Since biological research is increasingly probing ever-finer details of the cellular architecture, it is critical to understand the nanoscale transformation of the cellular organization due to fixation both systematically and quantitatively. In this work, we employed Partial Wave Spectroscopic (PWS) Microscopy, a nanoscale sensitive and label-free live cell spectroscopic-imaging technique, to analyze the effects of the fixation process through three commonly used fixation protocols for cells in vitro. In each method investigated, we detected dramatic difference in both nuclear and cytoplasmic nanoarchitecture between live and fixed states. But significantly, despite the alterations in cellular nanoscale organizations after chemical fixation, the population differences in chromatin structure (e.g. induced by a specific chemotherapeutic agent) remains. In conclusion, we demonstrated that the nanoscale cellular arrangement observed in fixed cells was fundamentally divorced from that in live cells, thus the quantitative analysis is only meaningful on the population level. This finding highlights the importance of live cell imaging techniques with nanoscale sensitivity or cryo-fixation in the interrogation of cellular structure, to complement more traditional chemical fixation methods.

Effect of calcium ions on the interactions between surfaces end-grafted with weak polyelectrolytes.

We study the interactions between two planar surfaces end-tethered with poly(acrylic acid) polymers in electrolyte solutions containing calcium ions, using a molecular theory. We found that by adding divalent calcium ions to an aqueous solution of monovalent ions leads to a dramatic reduction in the size and range of effective interactions between the two polymer layers. This is caused by the formation of favorable calcium bridges, i.e., complexes of one calcium ion and two carboxylic acid monomers, that reduce the effective charge of the polymer layers and, at sufficient calcium ion concentrations, can cause the polymer layers to collapse. For calcium ion concentrations above approximately 1 mM, the repulsions between the opposing end-grafted surfaces disappear and attractions occur. These attractions are correlated with the occurrence of interlayer divalent calcium bridges and do not occur for poly(acrylic acid) layers in contact with reservoir solutions containing only monovalent ions. This result indicates the suitability of divalent calcium ions to control and change the interaction range and strength, which is a useful property that is desirable in the design of stimuli-responsive nanomaterials.

Design of Multifunctional Nanogate in Response to Multiple External Stimuli Using Amphiphilic Diblock Copolymer.

Nature uses the interplay between hydrophobic and electrostatic interactions of disordered proteins to orchestrate complicated molecular gates such as the nuclear pore complex to control the transport of biological masses. Inspired by nature, we here theoretically show that well-defined gate shape, sensitive response to pH and salt concentration, and selectivity in cargo transport can be simultaneously achieved by grafting amphiphilic diblock copolymers made of sequence-controlled hydrophobic and ionizable monomers on the inner surface of solid-state nanopore. As a result, multiple functions such as ionic gating and molecular filtering can be implemented into one single copolymer nanogate. The gate structure and thermodynamics is a result of the self-assembly of the sequence-designed copolymer in the confined geometry that minimizes the free energy of the system. Our theory further predicts a phase transition and discontinuous charge regulation of the confined copolymer that allows logical gating in biosensors and nanofluidic devices. As an example of application, a nanolocker with the potential of molecular pumping has also been designed with the cooperation of two amphiphilic copolymer gates. Our results highlight the importance of polymer sequence in nanogating, and these insights can be used to guide the rational design of polymer-coated smart nanopores.

Membrane curvature enables N-Ras lipid anchor sorting to liquid-ordered membrane phases.

Trafficking and sorting of membrane-anchored Ras GTPases are regulated by partitioning between distinct membrane domains. Here, in vitro experiments and microscopic molecular theory reveal membrane curvature as a new modulator of N-Ras lipid anchor and palmitoyl chain partitioning. Membrane curvature was essential for enrichment in raft-like liquid-ordered phases; enrichment was driven by relief of lateral pressure upon anchor insertion and most likely affects the localization of lipidated proteins in general.

Structural behavior of competitive temperature and pH-responsive tethered polymer layers.

Herein, we develop a molecular theory to examine a class of pH and temperature-responsive tethered polymer layers. The response of pH depends on intramolecular charge repulsion of weakly acidic monomers and the response of temperature depends on hydrogen bonding between polymer monomers and water molecules akin to the behavior of water-soluble polymers such as PEG (poly-ethylene glycol) or NIPAAm (n-isopropylacrylamide). We investigate the changes in structural behavior that result for various end-tethered copolymers: pH/T responsive monomers alone, in alternating sequence with hydrophobic monomers, and as 50/50 diblocks with hydrophobic monomers. We find that the sequence and location of hydrophobic units play a critical role in the thermodynamic stability and structural behavior of these responsive polymer layers. Additionally, the polymers exhibit tunable collapse when varying the surface coverage, location and sequence of hydrophobic units as a function of temperature and pH. As far as we know, our results present the first molecularly detailed theory for end-tethered polymers that are both pH and temperature-responsive via hydrogen bonding. We propose that this work holds predictive power for the guided design of future biomaterials.

Dissipative self-assembly of particles interacting through time-oscillatory potentials.

Dissipative self-assembly is the emergence of order within a system due to the continuous input of energy. This form of nonequilibrium self-organization allows the creation of structures that are inaccessible in equilibrium self-assembly. However, design strategies for dissipative self-assembly are limited by a lack of fundamental understanding of the process. This work proposes a novel route for dissipative self-assembly via the oscillation of interparticle potentials. It is demonstrated that in the limit of fast potential oscillations the structure of the system is exactly described by an effective potential that is the time average of the oscillatory potential. This effective potential depends on the shape of the oscillations and can lead to effective interactions that are physically inaccessible in equilibrium. As a proof of concept, Brownian dynamics simulations were performed on a binary mixture of particles coated by weak acids and weak bases under externally controlled oscillations of pH. Dissipative steady-state structures were formed when the period of the pH oscillations was smaller than the diffusional timescale of the particles, whereas disordered oscillating structures were observed for longer oscillation periods. Some of the dissipative structures (dimers, fibers, and honeycombs) cannot be obtained in equilibrium (fixed pH) simulations for the same system of particles. The transition from dissipative self-assembled structures for fast oscillations to disordered oscillating structures for slow oscillations is characterized by a maximum in the energy dissipated per oscillation cycle. The generality of the concept is demonstrated in a second system with oscillating particle sizes.

Anisotropic surface functionalization of Au nanorods driven by molecular architecture and curvature effects.

This work suggests a novel strategy to coat the caps and body of Au-nanorods (Au-NRs) with end-grafted polymer layers of different compositions by taking advantage of the different curvature of these two regions. A molecular theory was used to theoretically investigate the effect of local curvature and molecular architecture (intramolecular connectivity of the monomers) on the adsorption of polymer mixtures on cylindrical (Au-NR body) and spherical (Au-NR caps) surfaces. The adsorption process was systematically studied as a function of the backbone length, number and position of branches, quality of the solvent and total number of monomers of the polymer molecules in the mixture. The balance between repulsive forces and polymer-surface and polymer-polymer attractions governs the amount and composition of the adsorbed layer. This balance is in turn modulated by the architecture of the polymers, the curvature of the surface and the competition between the different polymers in the mixture for the available area. As a result, the equilibrium composition of the polymer layer on spheres and cylinders of the same radius differs, and in turn departs from that of the bulk solution. Curvature plays a major role: the available volume at a given distance from the surface is larger for spherical surfaces than for cylindrical ones, therefore the surface density of the bulkier (more branched) polymer in the mixture is larger on the Au-NR caps than on the Au-NR body. These results suggest that the combination of curvature at the nanoscale and tailored molecular architecture can confer anisotropic nanoparticles with spatially enriched domains and, therefore, lead to nanoconstructs with directional chemical interactions.

Controlling swelling/deswelling of stimuli-responsive hydrogel nanofilms in electric fields.

The swelling/deswelling transition of pH-sensitive, electrode-grafted, hydrogel nanofilms when exposed to electric fields is studied by theoretical analysis. In acidic conditions, the response of these films to changes in pH is dominated by network-surface interactions, while intra-network electrostatic repulsions, which are highly modulated by the adsorption of salt ions, determine material response at a higher pH. Film thickness is a non-monotonic function of solution pH and displays a local maximum, a local minimum or both, depending on the salt concentration and the applied voltage. We suggest the use of these materials in the development of biosensors and control of enzyme activity.

Effect of charge, hydrophobicity, and sequence of nucleoporins on the translocation of model particles through the nuclear pore complex.

The molecular structure of the yeast nuclear pore complex (NPC) and the translocation of model particles have been studied with a molecular theory that accounts for the geometry of the pore and the sequence and anchoring position of the unfolded domains of the nucleoporin proteins (the FG-Nups), which control selective transport through the pore. The theory explicitly models the electrostatic, hydrophobic, steric, conformational, and acid-base properties of the FG-Nups. The electrostatic potential within the pore, which arises from the specific charge distribution of the FG-Nups, is predicted to be negative close to pore walls and positive along the pore axis. The positive electrostatic potential facilitates the translocation of negatively charged particles, and the free energy barrier for translocation decreases for increasing particle hydrophobicity. These results agree with the experimental observation that transport receptors that form complexes with hydrophilic/neutral or positively charged proteins to transport them through the NPC are both hydrophobic and strongly negatively charged. The molecular theory shows that the effects of electrostatic and hydrophobic interactions on the translocating potential are cooperative and nonequivalent due to the interaction-dependent reorganization of the FG-Nups in the presence of the translocating particle. The combination of electrostatic and hydrophobic interactions can give rise to complex translocation potentials displaying a combination of wells and barriers, in contrast to the simple barrier potential observed for a hydrophilic/neutral translocating particle. This work demonstrates the importance of explicitly considering the amino acid sequence and hydrophobic, electrostatic, and steric interactions in understanding the translocation through the NPC.

Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium.

Connections between microscopic dynamical observables and macroscopic nonequilibrium (NE) properties have been pursued in statistical physics since Boltzmann, Gibbs, and Maxwell. The simulations we describe here establish a relationship between the Kolmogorov-Sinai entropy and the energy dissipated as heat from a NE system to its environment. First, we show that the Kolmogorov-Sinai or dynamical entropy can be separated into system and bath components and that the entropy of the system characterizes the dynamics of energy dissipation. Second, we find that the average change in the system dynamical entropy is linearly related to the average change in the energy dissipated to the bath. The constant energy and time scales of the bath fix the dynamical relationship between these two quantities. These results provide a link between microscopic dynamical variables and the macroscopic energetics of NE processes.

How Does Confinement Change Ligand-Receptor Binding Equilibrium? Protein Binding in Nanopores and Nanochannels.

We present systematic studies for the binding of small model proteins to ligands attached to the inner walls of long nanochannels and short nanopores by polymeric tethers. Binding of proteins to specific ligands inside nanometric channels and pores leads to changes in their ionic conductance, which have been exploited in sensors that quantify the concentration of the proteins in solution. The theoretical predictions presented in this work are aimed to provide a fundamental understanding of protein binding under geometrically confined environments and to guide the design of this kind of nanochannel-based sensors. The theory predicts that the fraction of the channel volume filled by bound proteins is a nonmonotonic function of the channel radius, the length of the tethers, the surface density of the ligands and the size of the proteins. Notably, increasing the density of ligands, decreasing the size of the channel or increasing the size of the protein may lead to a decrease of the fraction of the channel volume filled by bound proteins. These results are explained from the incomplete binding of proteins to the ligands due to repulsive protein-protein and protein-ligand steric interactions. Our work suggests strategies to optimize the change in conductance due to protein binding, for example: (i) proteins much smaller than the radius of the channel may effectively block the channel if tethers of appropriate length are used, and (ii) a large decrease in conductance upon protein binding can be achieved if the channel and the protein are oppositely charged.